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2004 Fiscal Year Final Research Report Summary

Asymptotic analytical study of differential equations

Research Project

Project/Area Number 15540186
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionSophia University

Principal Investigator

UCHIYAMA Koichi  Sophia University, Mathematics, Professor, 理工学部, 教授 (20053689)

Co-Investigator(Kenkyū-buntansha) OUCHI Sunao  Sophia University, Mathematics, Professor, 理工学部, 教授 (00087082)
TAHARA Hidetoshi  Sophia University, Mathematics, Professor, 理工学部, 教授 (60101028)
YOSHINO Kunio  Sophia University, Mathematics, Lecturer, 理工学部, 講師 (60138378)
HIRATA Hitoshi  Sophia University, Mathematics, Assistant, 理工学部, 助手 (20266076)
AOYAGI Miki  Sophia University, Mathematics, Assistant, 理工学部, 助手 (90338434)
Project Period (FY) 2003 – 2004
Keywordsasymptotic analysis / Borel summable / multi-summable / Fuchsian equation / totally characteristic / A-elliptic / distribution with support in a cone / stochastic complexity
Research Abstract

A. Asymptotic analysis of differential equations in complex domain.
Uchiyama showed that formal solutions to a certain nonlinear PDE with regular singularity converge by the method of majorant series. Ouchi showed Borel summability of formal solutions to a certain semilinear 1^<st> order singular PDE and its application to normal form of vector fields and multi-summability of formal solution to a certain PDE regarded as perturbation of ODE. Tahara obtained the structure of singularities of solutions to Fuchsian nonlinear PDE, necessary or sufficient conditions for existence of singular solutions to 1St order PDE's of normal type and (non)existence of singularities and uniqueness of solutions to nonlinear PDE of totally characteristic type.
B. Asymptotic analysis of differential equations in real domain and related analysis.
Uchiyama showed local uniquness of radial solutions to 2^<nd> order one dimensional p-elliptic equations and obtained with L.Paredes a candidate of nonlinear PDEs with regular singularity from one dimensinal model of 4^<th> order p-elliptic equations. Yoshino, with M. Suwa, characterized distribution of exponential type with applications and obtained results on positive definite distribution. Hirata gave a concrete representation of a family of solutions through elliptic functions to 3^<rd> order nonlinear PDE. Goto did reserch on asymptotic inclusion. Aoyagi gave asymptotic expasion of the stochastic comlexity of non-analytic learning machines.

  • Research Products

    (10 results)

All 2005 2004 2003

All Journal Article (10 results)

  • [Journal Article] Borel summability of formal solutions of some first order singular patial differential equations and normal …2005

    • Author(s)
      S.Ouchi
    • Journal Title

      J.Math.Soc.Japan (to appear)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Borel summability of formal solutions of some first order singular partial differential equations and normal forms of vector fields2005

    • Author(s)
      S.Ouchi
    • Journal Title

      J.Math.Soc.Japan (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Pラプラシアンに同伴する非線形常微分方程式の解の特異性について2004

    • Author(s)
      内山 康一
    • Journal Title

      数学解析の望ましい姿を探って(九州大学出版会)

      Pages: 59-67

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A characterization of tempered distribution with support in a cone by the heat kernel method …2004

    • Author(s)
      M.Suwa, K.Yoshino
    • Journal Title

      J.Math.Sci.Univ.Tokyo 11

      Pages: 75-90

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Stochastic complexity and Newton diagram2004

    • Author(s)
      K.Yamazaki, M.Aoyagi, S.Watanabe
    • Journal Title

      Int.Symp.Information Theory and its Appl.ISITA 2004,Parma, Italy

      Pages: 105-110

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A characeteization of tempered distributions with support in a cone by the heat kernel method and its applications2004

    • Author(s)
      M.Suwa, K.Yoshino
    • Journal Title

      J.Math.Sci.Univ.Tokyo 11

      Pages: 75-90

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Stochastic complexity and Newton diagram2004

    • Author(s)
      K.Yamazaki, M.Aoyagi, S.Watanabe
    • Journal Title

      Int.Symp.Information Theory and it Appl.ISITA 2004 Parma Italy

      Pages: 105-110

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Solvability of partial differential equations of nonlinear totally characteristic type with resonance2003

    • Author(s)
      H.Tahara
    • Journal Title

      J.Math.Soc.Japan 55・4

      Pages: 1095-1113

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Analytic Singularities of Solutions to certain Nonlinear Ordinary differential Euqations associated with p-Laplacian2003

    • Author(s)
      L.Paredes, K.Uchiyama
    • Journal Title

      Tokyo J.Math. 26

      Pages: 229-240

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Solvability of partical differential equations of nonlinear totally characteristic type with resonance2003

    • Author(s)
      H.Tahara
    • Journal Title

      J.Math.Soc.Japan 55-4

      Pages: 1095-1113

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2006-07-11  

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